Simultaneous Effects p77 XGE

Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table-whether player or DM-who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character's turn, the player decides which of the two effects happens first.

NOT the turn controller, the creature controler. Though I am glad they fixed the wording in the later rewrite of shifter.  Though I do stand corrected on the barbarian.  I had missed the "Resistance and vulnerability" section in the book earlier, I just tried to find a similar example and picked a bad one.  The target of the abilities in this case is the defender who used their shifter ability on themselves and also blur/dodged themselves and is the target of the attack.  Its also why you round up healing and round down damage though they also explicitly stated that in the damage section for clarity too.

The shifter ability doesnt grant disadvantage canceling the advantge, it removes advantage.  The fact the target of the attack is trying to also apply disadvantage is irelavant as the target can choose either to cancel out advantage with disadvantage then do nothing to the attack because they arent attacking with advantage on a wildhunt shifter, or they can cancel advantage before the attack is rolled with wildhunt shift and then impose disadvantage to the attack with a dodge.  Since both effects target the shifter being hit The shifter would presumably always pick the latter (but who knows, maybe we have a massochistic shifter, or one who wants a cool dramatic death?  I'd' agree it was always a flat roll if it specificly said Wildhunt shift ability imposes disadvantage on attack rolls made within X feet or whatever as this would be covered by the 'multiple instances of advantage or disadvantage all cancel out without stacking'. It doesnt rather it specificly uses the wording to cancel advantage rather than saying specificly makes a flat roll.  I think this part was more telling.